### Archives

### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

Nonspecial tree 11P99 Almost-disjoint famiy Ostaszewski square Erdos-Hajnal graphs reflection principles Poset diamond star Postprocessing function ccc Absoluteness Souslin Tree free Boolean algebra coloring number Dushnik-Miller Coherent tree Singular Density Microscopic Approach Mandelbrot set stationary hitting Chromatic number middle diamond Hedetniemi's conjecture tensor product graph Partition Relations Forcing Axioms Singular cardinals combinatorics Cohen real Minimal Walks polarized partition relation weak diamond incompactness Knaster Non-saturation Club Guessing Singular coﬁnality Stevo Todorcevic Jonsson cardinal L-space PFA(S)[S] Square-Brackets Partition Relations Luzin set Hindman's Theorem stationary reflection xbox Forcing very good scale Selective Ultrafilter Successor of Singular Cardinal Kurepa Hypothesis Cardinal Invariants Axiom R Prevalent singular cardinals Cardinal function weak square square principles approachability ideal Ascent Path Small forcing Sakurai's Bell inequality Distributive tree square Almost Souslin Diamond Fodor-type reflection 05A17 Hereditarily Lindelöf space S-Space Uniformly coherent projective Boolean algebra super-Souslin tree Erdos Cardinal Rainbow sets OCA Large Cardinals Universal Sequences Slim tree b-scale Fat stationary set Almost countably chromatic Foundations Uniformization Generalized Clubs Prikry-type forcing Rock n' Roll Commutative cancellative semigroups Weakly compact cardinal Fast club Shelah's Strong Hypothesis Successor of Regular Cardinal HOD Reduced Power Martin's Axiom sap 20M14 Chang's conjecture Constructible Universe PFA Aronszajn tree P-Ideal Dichotomy Whitehead Problem Rado's conjecture Parameterized proxy principle Antichain

# Tag Archives: Singular Density

## On topological spaces of singular density and minimal weight

Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … Continue reading

## Workshop on Set Theory and its Applications, February 2007

These are the slides of a talk given at the Workshop on Set Theory and its Applications workshop (Weizmann Institute, February 19, 2007). Talk Title: Nets of spaces having singular density Abstract: The weight of a topological space X is the … Continue reading

## On the consistency strength of the Milner-Sauer conjecture

Abstract: In their paper from 1981, Milner and Sauer conjectured that for any poset $\mathbb P$, if $\text{cf}(\mathbb P)$ is a singular cardinal $\lambda$, then $\mathbb P$ must contain an antichain of size $\text{cf}(\lambda)$. The conjecture is consistent and known … Continue reading